Tetrahedral symmetry in Zr nuclei: Calculations of low-energy excitations with Gogny interaction

Abstract

We report on the results of the calculations of the low energy excitation patterns for three Zirconium isotopes, viz. ${}^{80}$Zr${}_{40}$, ${}^{96}$Zr${}_{56}$ and ${}^{110}$Zr${}_{70}$, reported by other authors to be doubly-magic tetrahedral nuclei (with tetrahedral magic numbers $Z$=40 and $N$=40, 56 and 70). We employ the realistic Gogny effective interactions using three variants of their parametrisation and the particle-number, parity and the angular-momentum projection techniques. We confirm quantitatively that the resulting spectra directly follow the pattern expected from the group theory considerations for the tetrahedral symmetric quantum objects. We also find out that, for all the nuclei studied, the correlation energy obtained after the angular momentum projection is very large for the tetrahedral deformation as well as other octupole deformations. The lowering of the energies of the resulting configurations is considerable, i.e. by about 10 MeV or even more, once again confirming the significance of the angular-momentum projections techniques in the mean-field nuclear structure calculations.

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Cited by in corpus (17)

• Mean field and beyond description of nuclear structure with the Gogny force: A review
• Tetrahedral shapes of neutron-rich Zr isotopes from multidimensionally-constrained relativistic Hartree-Bogoliubov model
• Ground state octupole correlation energies with effective forces
• Anatomy of octupole correlations in ${}^{96}$Zr with a symmetry-restored multidimensionally-constrained covariant density functional theory
• The impact of the surface energy coefficient on the deformation properties of atomic nuclei as predicted by Skyrme energy density functionals
• Spectroscopic Criteria for Identification of Nuclear Tetrahedral and Octahedral Symmetries: Illustration on a Rare Earth Nucleus
• Shape evolution of Zr nuclei and roles of tensor force
• Rotational motion of triaxially deformed nuclei studied by microscopic angular-momentum-projection method II: Chiral doublet band
• $g$-matrix folding-model approach to reaction cross sections for scattering of Ca isotopes on a C target
• Oxygen-16 Spectrum from Tetrahedral Vibrations and their Rotational Excitations
• Rotational motion of triaxially deformed nuclei studied by microscopic angular-momentum-projection method I: Nuclear wobbling motion
• Angular momentum projected multi-cranked configuration mixing for reliable calculation of high-spin rotational bands
• Infinitesimal cranking for triaxial angular-momentum-projected configuration-mixing calculation and its application to the gamma vibrational band
• Enlarged deformation region in neutron-rich Zr isotopes by the second intruder orbit
• First order Coriolis-coupling for rotational spectrum of a tetrahedrally-deformed core plus one-particle system
• Quantized Skyrmions from SU(4) Weight Diagrams
• Tetrahedral shape and Lambda impurity effect in ${}^{80}$Zr with a multidimensionally constrained relativistic Hartree-Bogoliubov model